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The aim of this paper is study the problem of longitudinal wave (p-wave) and secondary vertically (SV-wave) reflection and transmission during two media in the context of three magneto-thermoelastic theories with varies fields effects as magnetic field and initial stress.We deal the problem of reflection and transmission of thermoelastic waves at interface between two different media in the presence of initial stress and magnetic field, in the context of CT (Classical theory), GL (Green-Lindsay) and DPL (Dual Phase Lag). The boundary conditions applied at the interface as continuity of the displacement, neglecting the tangential displacement, continuity of normal force per unit initial area, neglecting the tangential stress and continuity of the temperature. The amplitudes ratios for the incident p- and SV- waves and so the refracted are obtained. The reflection and transmission coefficients ratios for the incident waves are computed numerically and the results are represented graphically to show the physical meaning of the phenomena.

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